Most likely the stoics (the classical stoics) had a plurality of beliefs related to mind/body dualism -- some believed in a pneuma or soul, some did not. All believed that we -- whether mind or body, were part of an ordered universe, one giant machine of matter and logic, so even if body and mind were believed to be separate, they are still both part of logos.

Whether the mind exists out of the body's matter notwithstanding, Epictetus considers the body as external and not under our control, he says it right on page one of The Enchiridion actually. Despite your best intentions and efforts, you could be effected by cancer or be in an accident, for example. Neither situation is in your control, or prevents you from cultivating virtue, so to be emotionally disturbed by such events is irrational.

I think what the modern stoic must acknowledge, moreso than neurobiology, is that we now know that in some cases it may not be possible to control our own mind and we may lose our faculties of reason. Dementia being the most clear example but someone may fall victim to psychological disorders as well. This is tough to come to terms with and I personally am not sure I have a solution.